Logo der Physikalisch-Technischen Bundesanstalt

Messunsicherheit

Arbeitsgruppe 8.42
Nach oben

Übersicht

Der Vergleich von Messergebnissen, zuverlässige Entscheidungsfindungen und Konformitätsbewertungen erfordern, dass Messergebnissen eine Unsicherheit beigeordnet wird. Die Möglichkeit des Vergleichs von Messergebnissen, die an verschiedenen Orten oder zu unterschiedlichen Zeiten erzielt wurden, ist zentral für die internationale Metrologie. Mit dem “Guide to the Expression of Uncertainty in Measurement” (Opens external link in new windowGUM) steht eine Anleitung zur Unsicherheitsermittlung zur Verfügung, die bereits in vielen Anwendungen der Metrologie erfolgreich eingesetzt wurde.

Illustration der Monte Carlo Methode gemäß Opens external link in new windowSupplement 1 to the GUM.

Im Rahmen ihrer jüngeren Entwicklung unterstützt die Metrologie zunehmend neue Themen, um gesellschaftlichen Herausforderungen in Umwelt und Klima, Lebenswissenschaften und Medizin begegnen zu können. Dabei spielen Bildgebung, Spektroskopie, Erdbeobachtungen und Sensornetzwerke eine zunehmend wichtige Rolle. Die zuverlässige Unsicherheitsermittlung ist in diesen Anwendungsfeldern besonders wichtig, etwa um die Diagnose eines Tumors abzusichern im Rahmen der quantitativen Bildgebung oder bei der Kontrolle von Umweltverschmutzungen. Der GUM wird allerdings den Herausforderungen in diesen Anwendungen nicht vollständig gerecht, und die Entwicklung statistischer Verfahren für eine verbesserte Unsicherheitsermittlung wird dringend benötigt.

Nach oben

Forschung

Der Schwerpunkt in der Arbeitsgruppe 8.42 der PTB liegt auf der Entwicklung Bayes’scher Verfahren zu Unsicherheitsermittlung. Diese Entwicklung wird im Zusammenhang mit unterschiedlichen Forschungsgebieten wie der „large-scale data analysis“ oder des „deep learning“ durchgeführt. Ebenso werden Bayes’sche Inferenzverfahren für eine mögliche Erweiterung der aktuellen GUM-Methodik in der Arbeitsgruppe 8.42 der PTB entwickelt. Beispiele hierfür sind einfache Verfahren, mit denen vorhandenes Vorwissen auf Priorverteilungen abgebildet werden kann, sowie Berechnungsmethoden. „Open source software“ wird bereitgestellt, um die Anwendung der entwickelten Verfahren zu erleichtern.

Nach oben

Software

Nach oben

Publikationen

•
K. Klauenberg, J. Greenwood and G. Foyer
Propagation of conformity statements in compliance with the GUM and ISO 17025.
Metrologia, 60(5),
054004,
2023.
[DOI: 10.1088/1681-7575/acf3eb]
•
S. Brahma, C. Kolbitsch, J. Martin, T. Schäffter and A. Kofler
Data-efficient Bayesian learning for radial dynamic MR reconstruction.
Medical Physics,
2023.
[DOI: 10.1002/mp.16543]
•
M. Marschall, G. Wübbeler, M. Borys and C. Elster
On modelling of artefact instability in interlaboratory comparisons.
Metrologia,
2023.
[DOI: 10.1088/1681-7575/ace18f]
•
G. Kok, v. M. Dijk, G. Wübbeler and C. Elster
Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry.
Metrologia,
2023.
[DOI: 10.1088/1681-7575/acd6fd]
•
G. Kok, G. Wübbeler and C. Elster
Impact of Imperfect Artefacts and the Modus Operandi on Uncertainty Quantification Using Virtual Instruments.
Metrology, 2
311--319,
2022.
[DOI: 10.3390/metrology2020019]
•
M. Marschall, S. Sievers, H. W. Schumacher and C. Elster
Uncertainty propagation in quantitative magnetic force microscopy using a Monte-Carlo method.
IEEE Transactions on Magnetics,
1--1,
2022.
[DOI: 10.1109/TMAG.2022.3153176]
•
M. Marschall, G. Wübbeler and C. Elster
Rejection sampling for Bayesian uncertainty evaluation using the Monte Carlo techniques of GUM-S1.
Metrologia, 59(1),
015004,
2022.
[DOI: 10.1088/1681-7575/ac3920]
•
M. Gruber, T. Dorst, A. Schütze, S. Eichstädt and C. Elster
Discrete wavelet transform on uncertain data: Efficient online implementation for practical applications..
Advanced Mathematical and Computational Tools in Metrology and Testing XII, Series on Advances in Mathematics for Applied Sciences, 90
2022.
•
S. Metzner
Bayesian data analysis for magnetic resonance fingerprinting.
PhD Thesis
2021.
[DOI: 10.14279/depositonce-12455]
•
J. Martin and C. Elster
GUI for Bayesian sample size planning in type A uncertainty evaluation.
Measurement Science and Technology, 32(7),
5005,
2021.
[DOI: 10.1088/1361-6501/abe2bd]
•
S. Metzner, G. Wübbeler, S. Flassbeck, C. Gatefait, C. Kolbitsch and C. Elster
Bayesian uncertainty quantification for magnetic resonance fingerprinting.
Physics in Medicine & Biology, 66(7),
075006,
2021.
[DOI: 10.1088/1361-6560/abeae7]
•
G. Wübbeler, M. Marschall and C. Elster
A simple method for Bayesian uncertainty evaluation in linear models.
Metrologia, 57(6),
065010,
2020.
[DOI: 10.1088/1681-7575/aba3b8]
•
J. Martin and C. Elster
The variation of the posterior variance and Bayesian sample size determination.
Statistical Methods & Applications,
1613-981X,
2020.
[DOI: 10.1007/s10260-020-00545-3]
•
S. Demeyer, N. Fischer and C. Elster
Guidance on Bayesian uncertainty evaluation for a class of GUM measurement models.
Metrologia,
2020.
[DOI: 10.1088/1681-7575/abb065]
•
G. Bartl, C. Elster, J. Martin, R. Schödel, M. Voigt and A. Walkov
Thermal expansion and compressibility of single-crystal silicon between 285 K and 320 K.
Measurement Science and Technology, 31(6),
2020.
[DOI: 10.1088/1361-6501/ab7359]
•
G. Wübbeler and C. Elster
On the transferability of the GUM-S1 type A uncertainty.
Metrologia, 57(1),
2020.
[DOI: 10.1088/1681-7575/ab50d6]
•
K. Klauenberg, G. Wübbeler and C. Elster
About not Correcting for Systematic Effects.
Measurement Science Review, 19(5),
204--208,
2019.
[DOI: 10.2478/msr-2019-0026]
•
S. Metzner, G. Wübbeler and C. Elster
Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging.
AStA Adv Stat Anal, 103(3),
333--355,
2019.
[DOI: 10.1007/s10182-018-00334-0]
•
J. Martin, G. Bartl and C. Elster
Application of Bayesian model averaging to the determination of thermal expansion of single-crystal silicon.
Measurement Science and Technology, 30
045012,
2019.
[DOI: 10.1088/1361-6501/ab094b]
•
O. Bodnar and C. Elster
Assessment of vague and noninformative priors for Bayesian estimation of the realized random effects in random-effects meta-analysis.
AStA Advances in Statistical Analysis, 102(1),
1--20,
2018.
[DOI: 10.1007/s10182-016-0279-7]
•
G. Wübbeler, O. Bodnar and C. Elster
Robust Bayesian linear regression with application to an analysis of the CODATA values for the Planck constant.
Metrologia, 55(1),
20,
2018.
[DOI: 10.1088/1681-7575/aa98aa]
•
F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling and C. Elster
Uncertainty evaluation and propagation for spectral measurements.
Color, Research and Application, 43(1),
6--16,
2017.
[DOI: 10.1002/col.22185]
•
M. Reginatto, M. Anton and C. Elster
Assessment of CT image quality using a Bayesian approach.
Metrologia, 54(4),
S74--S82,
2017.
[DOI: 10.1088/1681-7575/aa735b]
•
S. Eichstädt and V. Wilkens
Evaluation of uncertainty for regularized deconvolution: A case study in hydrophone measurements.
J. Acoust. Soc. Am., 141(6),
4155--4167,
2017.
[DOI: 10.1121/1.4983827]
•
O. Bodnar, R. Behrens and C. Elster
Bayesian inference for measurements of ionizing radiation under partial information.
Metrologia, 54(3),
S29--S33,
2017.
[DOI: 10.1088/1681-7575/aa69ad]
•
S. Eichstädt, C. Elster, I. M. Smith and T. J. Esward
Evaluation of dynamic measurement uncertainty – an open-source software package to bridge theory and practice.
J. Sens. Sens. Syst., 6
97-105,
2017.
[DOI: 10.5194/jsss-6-97-2017]
•
O. Bodnar, A. Link, B. Arendacká, A. Possolo and C. Elster
Bayesian estimation in random effects meta-analysis using a non-informative prior.
Statistics in Medicine, 39(2),
378--399,
2017.
[DOI: 10.1002/sim.7156]
•
K. Klauenberg and C. Elster
Sampling for assurance of future reliability.
Metrologia, 54(1),
59--68,
2017.
[DOI: 10.1088/1681-7575/54/1/59]
•
G. Wübbeler, J. Campos Acosta and C. Elster
Evaluation of uncertainties for CIELAB color coordinates.
Color Research & Application,
2016.
[DOI: 10.1002/col.22109]
•
O. Bodnar, C. Elster, J. Fischer, A. Possolo and B. Toman
Evaluation of uncertainty in the adjustment of fundamental constants.
Metrologia, 53(1),
S46,
2016.
[DOI: 10.1088/0026-1394/53/1/S46]
[http://stacks.iop.org/0026-1394/53/i=1/a=S46]
•
K. Klauenberg and C. Elster
Markov chain Monte Carlo methods: an introductory example.
Metrologia, 53(1),
S32,
2016.
[DOI: 10.1088/0026-1394/53/1/S32]
[http://stacks.iop.org/0026-1394/53/i=1/a=S32]
•
C. Elster and G. Wübbeler
Bayesian regression versus application of least squares—an example.
Metrologia, 53(1),
S10,
2016.
[DOI: 10.1088/0026-1394/53/1/S10]
[http://stacks.iop.org/0026-1394/53/i=1/a=S10]
•
O. Bodnar, A. Link and C. Elster
Objective Bayesian Inference for a Generalized Marginal Random Effects Model.
Bayesian Analysis, 11(1),
25-45,
2016.
[DOI: 10.1214/14-BA933]
[http://projecteuclid.org/euclid.ba/1423083638]
(Open Access)
•
K. Klauenberg, G. Wübbeler, B. Mickan, P. Harris and C. Elster
A tutorial on Bayesian Normal linear regression.
Metrologia, 52(6),
878--892,
2015.
[DOI: 10.1088/0026-1394/52/6/878]
•
C. Elster, K. Klauenberg, M. Walzel, P. M. Harris, M. G. Cox, C. Matthews, L. Wright, A. Allard, N. Fischer, S. Ellison, P. Wilson, F. Pennecchi, G. J. P. Kok, A. Van der Veen and L. Pendrill
A Guide to Bayesian Inference for Regression Problems.
EMRP NEW04,
2015.
[http://www.ptb.de/emrp/new04.html]
•
G. Wübbeler, O. Bodnar, B. Mickan and C. Elster
Explanatory power of degrees of equivalence in the presence of a random instability of the common measurand.
Metrologia, 52(2),
400--405,
2015.
[DOI: 10.1088/0026-1394/52/2/400]
[http://iopscience.iop.org...0.1088/0026-1394/52/2/400]
•
G. J. P. Kok, A. M. H. van der Veen, P. M. Harris, I. M. Smith and C. Elster
Bayesian analysis of a flow meter calibration problem.
Metrologia, 52(2),
392-399,
2015.
[DOI: 10.1088/0026-1394/52/2/392]
[http://iopscience.iop.org...0.1088/0026-1394/52/2/392]
•
A. Possolo and C. Elster
Evaluating the uncertainty of input quantities in measurement models.
Metrologia, 51(3),
339--353,
2014.
[DOI: 10.1088/0026-1394/51/3/339]
[http://iopscience.iop.org...0.1088/0026-1394/51/3/339]
•
O. Bodnar and C. Elster
Analytical derivation of the reference prior by sequential maximization of Shannon's mutual information in the multi-group parameter case.
Journal of Statistical Planning and Inference, 147
106--116,
2014.
[DOI: 10.1016/j.jspi.2013.11.003]
[http://www.sciencedirect....cle/pii/S0378375813002802]
•
O. Bodnar and C. Elster
On the adjustment of inconsistent data using the Birge ratio.
Metrologia, 51(5),
516--521,
2014.
[DOI: 10.1088/0026-1394/51/5/516]
[http://iopscience.iop.org...0.1088/0026-1394/51/5/516]
•
B. Arendacká, A. Täubner, S. Eichstädt, T. Bruns and C. Elster
Linear Mixed Models: Gum and Beyond.
Measurement Science Review, 14(2),
52-61,
2014.
[DOI: 10.2478/msr-2014-0009]
[http://www.degruyter.com/...14-0009/msr-2014-0009.xml]
•
S. J. Haslett, S. Puntanen and B. Arendacká
The link between the mixed and fixed linear models revisited.
Statistical Papers, 56(3),
849--861,
2014.
[DOI: 10.1007/s00362-014-0611-9]
[http://link.springer.com/10.1007/s00362-014-0611-9]
•
C. Elster
Bayesian uncertainty analysis compared with the application of the GUM and its supplements.
Metrologia, 51(4),
S159--S166,
2014.
[DOI: 10.1088/0026-1394/51/4/S159]
[http://iopscience.iop.org....1088/0026-1394/51/4/S159]
•
G. Wübbeler and C. Elster
Simplified evaluation of magnetic field fluctuation thermometry.
Measurement Science and Technology, 24(11),
115004,
2013.
[DOI: 10.1088/0957-0233/24/11/115004]
[http://iopscience.iop.org...88/0957-0233/24/11/115004]
•
S. Eichstädt, A. Link, P. M. Harris and C. Elster
Efficient implementation of a Monte Carlo method for uncertainty evaluation in dynamic measurements.
Metrologia, 49(3),
401,
2012.
[DOI: 10.1088/0026-1394/49/3/401]
•
K. Klauenberg and C. Elster
The multivariate normal mean - sensitivity of its objective Bayesian estimates.
Metrologia, 49(3),
395--400,
2012.
[DOI: 10.1088/0026-1394/49/3/395]
[http://iopscience.iop.org...0.1088/0026-1394/49/3/395]
•
G. Wübbeler, F. Schmähling, J. Beyer, J. Engert and C. Elster
Analysis of magnetic field fluctuation thermometry using Bayesian inference.
Measurement Science and Technology, 23(12),
125004,
2012.
[DOI: 10.1088/0957-0233/23/12/125004]
[http://iopscience.iop.org...88/0957-0233/23/12/125004]
•
W. Bich, M. G. Cox, R. Dybkaer, C. Elster, W. T. Estler, B. Hibbert, H. Imai, W. Kool, C. Michotte, L. Nielsen, L. Pendrill, S. Sidney, A. M. H. van der Veen and W. Wöger
Revision of the "Guide to the Expression of Uncertainty in Measurement".
Metrologia, 49(6),
702--705,
2012.
[DOI: 10.1088/0026-1394/49/6/702]
[http://iopscience.iop.org...0.1088/0026-1394/49/6/702]
•
C. Elster and I. Lira
On the choice of a noninformative prior for Bayesian inference of discretized normal observations.
Computational Statistics, 27(2),
219--235,
2012.
[DOI: 10.1007/s00180-011-0251-7]
[http://link.springer.com/10.1007/s00180-011-0251-7]
•
G. Wübbeler, P. M. Harris, M. G. Cox and C. Elster
Assessment of the GUM S1 Adaptive Monte Carlo Scheme.
In F. Pavese, M. Bär, J.M. Limares, C. Perruchet, N.F. Zhang, Editor, Band Advanced Mathematical & Computational Tools in Metrology IX aus Series on Advances in Mathematics for Applied Sciences
Kapitel 54, Seite 434
Herausgeber: World Scientific New Jersey,
84 Edition
2012.
•
S. Eichstädt and C. Elster
Uncertainty evaluation for continuous-time measurements.
In F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill, K. Shirono, Editor, Band Advanced Mathematical & Computational Tools in Metrology and Testing IX  aus Series on Advances in Mathematics for Applied Sciences
Kapitel 16, Seite 126-135
Herausgeber: World Scientific New Jersey,
84 Edition
2012.
•
T. J. Esward, C. Matthews, S. Downes, A. Knott, S. Eichstädt and C. Elster
Uncertainty evaluation for traceable dynamic measurement of mechanical quantities: A case study in dynamic pressure calibration.
In F. Pavese, M. Bär, J.-R. Filtz, A. B. Forbes, L. Pendrill, K. Shirono, Editor, Band Advanced Mathematical & Computational Tools in Metrology and Testing IX   aus Series on Advances in Mathematics for Applied Sciences
Kapitel 19, Seite 143-151
Herausgeber: World Scientific New Jersey,
84 Edition
2012.
•
O. Bodnar, G. Wübbeler and C. Elster
On the application of Supplement 1 to the GUM to non-linear problems.
Metrologia, 48(5),
333--342,
2011.
[DOI: 10.1088/0026-1394/48/5/014]
[http://iopscience.iop.org...0.1088/0026-1394/48/5/014]
•
C. Elster and B. Toman
Bayesian uncertainty analysis for a regression model versus application of GUM Supplement 1 to the least-squares estimate.
Metrologia, 48(5),
233--240,
2011.
[DOI: 10.1088/0026-1394/48/5/001]
[http://iopscience.iop.org...0.1088/0026-1394/48/5/001]
•
G. Wübbeler, P. M. Harris, M. G. Cox and C. Elster
A two-stage procedure for determining the number of trials in the application of a Monte Carlo method for uncertainty evaluation.
Metrologia, 47(3),
317--324,
2010.
[DOI: 10.1088/0026-1394/47/3/023]
[http://iopscience.iop.org...0.1088/0026-1394/47/3/023]
•
S. Eichstädt, A. Link, T. Bruns and C. Elster
On-line dynamic error compensation of accelerometers by uncertainty-optimal filtering.
Measurement, 43(5),
708-713,
2010.
[DOI: 10.1016/j.measurement.2009.12.028]
[http://www.sciencedirect....cle/pii/S0263224110000023]
•
A. Link and C. Elster
Uncertainty evaluation for IIR (infinite impulse response) filtering using a state-space approach.
Measurement Science and Technology, 20(5),
055104,
2009.
[DOI: 10.1088/0957-0233/20/5/055104]
•
C. Elster and B. Toman
Bayesian uncertainty analysis under prior ignorance of the measurand versus analysis using the Supplement 1 to the Guide : a comparison.
Metrologia, 46(3),
261--266,
2009.
[DOI: 10.1088/0026-1394/46/3/013]
[http://iopscience.iop.org...0.1088/0026-1394/46/3/013]
•
I. Lira, C. Elster, W. Wöger and M. G. Cox
Derivation of an output PDF from Bayes theorem and the principle of maximum entropy.
In F. Pavese, M. Bär, J.M. Limares, C. Perruchet, N.F. Zhang, Editor, Band Advanced Mathematical & Computational Tools in Metrology VIII aus Series on Advances in Mathematics for Applied Sciences
Kapitel 31, Seite 213
Herausgeber: World Scientific New Jersey,
78 Edition
2009.
•
G. Wübbeler, A. Link, T. Bruns and C. Elster
Impact of correlation in the measured frequency response on the results of a dynamic calibration.
In F. Pavese, M. Bär, J.M. Limares, C. Perruchet, N.F. Zhang, Editor, Band Advanced Mathematical & Computational Tools in Metrology VIII aus Series on Advances in Mathematics for Applied Sciences
Kapitel 52, Seite 369-374
Herausgeber: World Scientific New Jersey,
78 Edition
2009.
•
C. Elster and A. Link
Analysis of dynamic measurements: compensation of dynamic error and evaluation of uncertainty.
In F. Pavese, M. Bär, J.M. Limares, C. Perruchet, N.F. Zhang, Editor, Band Advanced Mathematical & Computational Tools in Metrology VIII aus Series on Advances in Mathematics for Applied Sciences
Kapitel 13, Seite 80-89
Herausgeber: World Scientific New Jersey,
78 Edition
2009.
•
G. Wübbeler, M. Krystek and C. Elster
Evaluation of measurement uncertainty and its numerical calculation by a Monte Carlo method.
Measurement Science and Technology, 19(8),
084009,
2008.
[DOI: 10.1088/0957-0233/19/8/084009]
[http://iopscience.iop.org...088/0957-0233/19/8/084009]
•
C. Elster and A. Link
Uncertainty evaluation for dynamic measurements modelled by a linear time-invariant system.
Metrologia, 45(4),
464-473,
2008.
[DOI: 10.1088/0026-1394/45/4/013]
•
I. Lira, C. Elster and W. Wöger
Probabilistic and least-squares inference of the parameters of a straight-line model.
Metrologia, 44(5),
379--384,
2007.
[DOI: 10.1088/0026-1394/44/5/014]
[http://iopscience.iop.org...0.1088/0026-1394/44/5/014]
•
C. Elster, W. Wöger and M. G. Cox
Draft GUM Supplement 1 and Bayesian analysis.
Metrologia, 44(3),
L31--L32,
2007.
[DOI: 10.1088/0026-1394/44/3/N03]
[http://iopscience.iop.org...0.1088/0026-1394/44/3/N03]
•
C. Elster, A. Link and T. Bruns
Analysis of dynamic measurements and determination of time-dependent measurement uncertainty using a second-order model.
Measurement Science and Technology, 18(12),
3682-3687,
2007.
[DOI: 10.1088/0957-0233/18/12/002]
•
C. Elster
Calculation of uncertainty in the presence of prior knowledge.
Metrologia, 44(2),
111--116,
2007.
[DOI: 10.1088/0026-1394/44/2/002]
[http://iopscience.iop.org...0.1088/0026-1394/44/2/002]
•
C. Elster, F. Schubert, A. Link, M. Walzel, F. Seifert and H. Rinneberg
Quantitative magnetic resonance spectroscopy: semi-parametric modeling and determination of uncertainties.
Magnetic resonance in medicine, 53(6),
1288--96,
2005.
[DOI: 10.1002/mrm.20500]
[http://www.ncbi.nlm.nih.gov/pubmed/15906296]
Export als:
BibTeX, XML
Nach oben